Answering Schrödinger's question: A free-energy formulation

Abstract

The free-energy principle (FEP) is a formal model of neuronal processes that is widely recognised in neuroscience as a unifying theory of the brain and biobehaviour. More recently, however, it has been extended beyond the brain to explain the dynamics of living systems, and their unique capacity to avoid decay. The aim of this review is to synthesise these advances with a meta-theoretical ontology of biological systems called variational neuroethology, which integrates the FEP with Tinbergen's four research questions to explain biological systems across spatial and temporal scales. We exemplify this framework by applying it to Homo sapiens, before translating variational neuroethology into a systematic research heuristic that supplies the biological, cognitive, and social sciences with a computationally tractable guide to discovery.

Keywords: Complex adaptive systems; Evolutionary systems theory; Free energy principle; Hierarchically mechanistic mind; Physics of the mind; Variational neuroethology.

Fig. 1

The free energy principle. (A) Schematic of the quantities that define free-energy. These include the internal states of a system μ (e.g. a brain) and quantities describing exchange with the world; namely, sensory input s = g(η,a)+ω and action a that changes the way the environment is sampled. The environment is described by equations of motion, $\dot{\eta }=f(\eta ,a)+\omega$, that specify the dynamics of (hidden) states of the world η. Here, ω denote random fluctuations. Internal states and action both change to minimise free-energy, which is a function of sensory input and a probabilistic representation (variational density) q(η:μ) encoded by the internal states. (B): Alternative expressions for the free-energy illustrating what its minimisation entails. For action, free-energy can only be suppressed by increasing the accuracy of sensory data (i.e., selectively sampling data that are predicted). Conversely, optimising internal states make the representation an approximate conditional density on the causes of sensory input (by minimising divergence). This optimisation makes the free-energy bound on surprise tighter and enables action to avoid surprising sensations.

Fig. 2

Variational neuroethology. (A) The meta-theoretical ontology we propose, called ‘variational neuroethology’, uses the FEP to explain and predict how living systems instantiate adaptive free energy minimisation. We have indicated some scales at which free energy minimizing dynamics unfold. Since spatial and temporal scales are intrinsically correlated (i.e., events unfolding over long distances usually take more time to unfold), what we have is a scale space that is populated mostly along its diagonal , , . (B) Equivalence classes of variational free energy minimizing systems. The free energy minimising dynamics at play are implemented by different kinds of mechanisms in different individual organisms and species, as a function of the coupling between their evolved phenotypes and biobehavioural patterns and the niches they inhabit and the scales under scrutiny. The gauge theoretical formalism for the FEP allows us to computationally model the regions of the biotic phase space, along its diagonal, that are apt to realize equivalent classes of dynamics. From .

Fig. 3

Nested Markov blankets. This schematic illustrates the hierarchical construction of (scale-free) compositions of Markov blankets of Markov blankets. The idea here is that particles, cells or subsystems at one scale (each comprising a Markov blanket $b_j^{(i)}$ that enshrouds internal states ${\mu }_j^{(i)}$) constitute an ensemble of states with a sparse dependency structure, which induces a Markov blanket at the supraordinate scale. This allows one to construct Markov blankets of Markov blankets by (i) partitioning the states at one level into a series of internal subsets and their Markov blankets and (ii) creating states for the next level by taking mixtures of Markov blanket states. Note that the internal states can be ignored when going from one level to the next because they are conditionally independent of external states (i.e., mixtures of Markov blankets from other subsystems). The mixtures can be regarded as slow (unstable) modes that are referred to as order parameters in synergetics . Filled (cyan) circles correspond to Markov blanket states at the i-th scale, where, as in Fig. 1, red denote sensory states and blue active states. The pictures (of Broccoli) in the upper panels illustrate the self similarity of this recursive partitioning. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)

Fig. 4

The hierarchically mechanistic mind. (A) Schematic of the multiscale hierarchical organisation of brain networks. Neural networks are composed of nodes and their connections, called edges. A node, defined as an interacting unit of a network, is itself a network composed of smaller nodes interacting at a lower hierarchical level, producing nested neural networks that extend from neurons, to macrocolumns, and to macroscopic brain regions. From . (B) A simple cortical hierarchy with ascending prediction errors and descending predictions. Superficial pyramidal cells (red triangles) compare expectations (at each level) with top-down predictions from deep pyramidal cells (black triangles) at higher levels. Neuromodulatory gating or gain control (blue) of superficial pyramidal cells determines their relative influence on the deep pyramidal cells that encode expectations by modulating their precision. From . (C): The variational neuroethology of human cognition and biobehaviour. $F(\tilde{s}(a),{\mu }^{(i)}|m^{(i)})$ represents the free-energy of the sensory data (over time), $\tilde{s}(a)$, and the states μ of an agent m⁽ⁱ⁾ ∈ s that belongs to a subgroup s ∈ c of class c. Action (a) governs the sampling of sensory data, and the physical states of the phenotype (μ) encode beliefs or expectations (and expectations of the mean of a probability distribution). Free energy minimisation dynamics vary across timescales, ranging from neurocognition in real-time (i.e., perception and action; learning and attention); neurodevelopment throughout the lifespan; epigenetic mechanisms that minimise free energy across generations (e.g., kin); and the process of adaptation, which involves the optimisation of human generative models over time and conspecifics via the inheritance of adaptive priors . These temporal processes are captured by Tinbergen's four levels of inquiry, which appeal to a dynamic causal hierarchy that is encapsulated by complementary paradigms in psychology: evolutionary psychology; evolutionary developmental approaches; developmental psychology; and the psychological subdisciplines , . (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)

Fig. 4

The hierarchically mechanistic mind. (A) Schematic of the multiscale hierarchical organisation of brain networks. Neural networks are composed of nodes and their connections, called edges. A node, defined as an interacting unit of a network, is itself a network composed of smaller nodes interacting at a lower hierarchical level, producing nested neural networks that extend from neurons, to macrocolumns, and to macroscopic brain regions. From . (B) A simple cortical hierarchy with ascending prediction errors and descending predictions. Superficial pyramidal cells (red triangles) compare expectations (at each level) with top-down predictions from deep pyramidal cells (black triangles) at higher levels. Neuromodulatory gating or gain control (blue) of superficial pyramidal cells determines their relative influence on the deep pyramidal cells that encode expectations by modulating their precision. From . (C): The variational neuroethology of human cognition and biobehaviour. $F(\tilde{s}(a),{\mu }^{(i)}|m^{(i)})$ represents the free-energy of the sensory data (over time), $\tilde{s}(a)$, and the states μ of an agent m⁽ⁱ⁾ ∈ s that belongs to a subgroup s ∈ c of class c. Action (a) governs the sampling of sensory data, and the physical states of the phenotype (μ) encode beliefs or expectations (and expectations of the mean of a probability distribution). Free energy minimisation dynamics vary across timescales, ranging from neurocognition in real-time (i.e., perception and action; learning and attention); neurodevelopment throughout the lifespan; epigenetic mechanisms that minimise free energy across generations (e.g., kin); and the process of adaptation, which involves the optimisation of human generative models over time and conspecifics via the inheritance of adaptive priors . These temporal processes are captured by Tinbergen's four levels of inquiry, which appeal to a dynamic causal hierarchy that is encapsulated by complementary paradigms in psychology: evolutionary psychology; evolutionary developmental approaches; developmental psychology; and the psychological subdisciplines , . (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)